Question: Simplify the following expression: $p = \dfrac{-55y^2}{-11y^3 + 77y^2}$ You can assume $y \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-55y^2 = - (5\cdot11 \cdot y \cdot y)$ The denominator can be factored: $-11y^3 + 77y^2 = - (11 \cdot y \cdot y \cdot y) + (7\cdot11 \cdot y \cdot y)$ The greatest common factor of all the terms is $11y^2$ Factoring out $11y^2$ gives us: $p = \dfrac{(11y^2)(-5)}{(11y^2)(-y + 7)}$ Dividing both the numerator and denominator by $11y^2$ gives: $p = \dfrac{-5}{-y + 7}$